Enable users to choose whether or not to use conditional dropdown logic

The solution is to make a total of three relationship.  You already have one of them.
Make a new relationships and for this one do not make it a Conditional Drop Down.

Then make a new calculated reference field such as [Related Parent (final)]

if([CDD related parent] >0, [CDD related parent], [non CDD related parent])

Then make a relationships on that field and get all your lookup fields from that relationship.

That will mean looking for the usage of the existing lookups and replacing their usage with the new lookups.  Then deleting them.